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arXiv:cond-mat/0610543 · Journal of Physics Condensed Matter

Driving a first order quantum phase transition by coupling a quantum dot to a 1D charge density wave

Y Weiss, M Goldstein, Richard Berkovits

Published Feb 9, 2007• 6 citations
arXivHTMLPDF

Abstract

The ground state properties of a one-dimensional system with particle–hole symmetry, consisting of a gate controlled dot coupled to an interacting reservoir, are explored using the numerical DMRG method. It has previously been shown that the system's thermodynamic properties as a function of the gate voltage in the Luttinger liquid phase are qualitatively similar to the behaviour of a non-interacting wire with an effective (renormalized) dot–lead coupling. Here we examine the thermodynamic properties of the wire in the charge density wave phase, and show that these properties behave quite differently. The number of electrons in the system remains constant as a function of the gate voltage, while the total energy becomes linear. Moreover, by tuning the gate voltage on the dot in the charge density wave phase it is possible to drive the wire through a first order quantum phase transition in which the population of each site in the wire is inverted.

DOI
10.1088/0953-8984/19/8/086215

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The ground state properties of a one-dimensional system with particle–hole symmetry, consisting of a gate controlled dot coupled to an interacting reservoir, are explored using the numerical DMRG method. It has previously been shown that the system's thermodynamic properties as a function of the gate voltage in the Luttinger liquid phase are qualitatively similar to the behaviour of a non-interacting wire with an effective (renormalized) dot–lead coupling. Here we examine the thermodynamic properties of the wire in the charge density wave phase, and show that these properties behave quite differently. The number of electrons in the system remains constant as a function of the gate voltage, while the total energy becomes linear. Moreover, by tuning the gate voltage on the dot in the charge density wave phase it is possible to drive the wire through a first order quantum phase transition in which the population of each site in the wire is inverted.
The effects of doping on a one-dimensional wire in a charge density wave state are studied using the density-matrix renormalization group method. We show that for a finite number of extra electrons, the ground state becomes conducting but the particle density along the wire corresponds to a charge density wave with an incommensurate+ wave number determined by the filling. We find that the absence of the translational invariance can be discerned even in the thermodynamic limit as long as the number of doping electrons is finite. The Luttinger liquid behavior is reached only for a finite change in the electron filling factor, which for an infinite wire corresponds to the addition of an infinite number of electrons. In addition to the half filled insulating Mott state and the conducting states, we find evidence for subgap states at fillings different from half filling by a single electron or hole. Finally, we show that by coupling our system to a quantum dot, one can have a discontinuous dependence of its population on the applied gate voltage in the thermodynamic limit, similar to the one predicted for a Luttinger liquid without umklapp processes.
We study a quantum phase transition that occurs in a system composed of two impurities (or quantum dots), each coupled to a different interacting (Luttinger liquid) lead. While the impurities are coupled electrostatically, there is no tunneling between them. Using a mapping of this system onto a Kondo model, we show analytically that the system undergoes a Berezinskii-Kosterlitz-Thouless quantum phase transition as a function of the Luttinger liquid parameter in the leads and the dot-lead interaction. The phase with low values of the Luttinger liquid parameter is characterized by an abrupt switch of the population between the impurities as a function of a common applied gate voltage. However, this behavior is hard to verify numerically since one would have to study extremely long systems. Interestingly, though, at the transition the entanglement entropy drops from a finite value of ln(2)\mathrm{ln}(2)ln(2) to zero. The drop becomes sharp for infinite systems. One can employ finite-size scaling to extrapolate the transition point and the behavior in its vicinity from the behavior of the entanglement entropy in moderate size samples. We employ the density matrix renormalization-group numerical procedure to calculate the entanglement entropy of systems with lead lengths of up to 480 sites. Using finite-size scaling, we extract the transition value and show it to be in good agreement with the analytical prediction.
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The dissipation induced by a metallic gate on the low-energy properties of interacting 1D electron liquids is studied. As a function of the distance to the gate, or the electron density in the wire, the system can undergo a quantum phase transition from a Tomonaga-Luttinger liquid to two kinds of dissipative phases, one of them with a finite spatial correlation length. We also define a dual model, which describes an attractive one-dimensional metal with a Josephson coupling to a dirty metallic lead.
Abstract The influence of nearest neighbor interactions in a reservoir coupled to a single level dot on the width of the level is studied, using the density matrix renormalization group (DMRG) method. We find that while in the Luttinger liquid (LL) phase of the lead (i.e., for weak interactions) the interactions cause a gradual decrease of the resonance width, in the charge density wave (CDW) phase (for strong interactions) the width is zero, and a sharp jump of the dot population occurs. We explain the physical difference between both cases. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An interacting spinless fermion wire coupled to a three-dimensional (3D) semiconducting substrate is approximated by a narrow ladder model (NLM) with varying number of legs. We compute density distributions, gaps, charge density wave (CDW) order parameters, correlation functions, and the central charge using the density-matrix renormalization group method. Three ground-state phases are observed: a one-component Luttinger liquid, a quasi-one-dimensional (1D) CDW insulator, and a band insulator. We investigated the convergence of the NLM properties with increasing number of legs systematically and confirm that the NLM is a good approximation for the quasi-1D phases (Luttinger liquid and CDW) of the 3D wire-substrate model. The quantum phase transitions between these phases are investigated as function of the coupling between wire and substrate. The critical nearest-neighbor interaction increases with increasing coupling between wire and substrate and thus the substrate stabilizes the Luttinger liquid in the wire. Our study confirms that a Luttinger liquid or CDW insulator phase could occur in the low-energy properties of atomic wires deposited on semiconducting substrates.